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%JSINGU Show the linearly dependent joints in a Jacobian matrix
%
% JSINGU(J) displays the linear dependency of joints in a Jacobian matrix.
% This dependency indicates joint axes that are aligned and causes singularity.
%
% See also SerialLink.jacobn.
% Copyright (C) 1993-2015, by Peter I. Corke
%
% This file is part of The Robotics Toolbox for MATLAB (RTB).
%
% RTB is free software: you can redistribute it and/or modify
% it under the terms of the GNU Lesser General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% RTB is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU Lesser General Public License for more details.
%
% You should have received a copy of the GNU Leser General Public License
% along with RTB. If not, see <http://www.gnu.org/licenses/>.
%
% http://www.petercorke.com
function jsingu(J)
% convert to row-echelon form
[R, jb] = rref(J);
depcols = setdiff( 1:numcols(J), jb);
fprintf('%d linearly dependent joints:\n', length(depcols));
for d=depcols
fprintf(' q%d depends on: ', d)
for k=find(R(:,d))
fprintf('q%d ', k);
end
fprintf('\n');
end